Stoke had winger Geoff McGaw sent off for a straight red-card offence after only 22 minutes after an altercation with Leeds' Scott Gardner after appearing to push his opponent.
United were already ahead after an 18th-minute goal from Jonny Howson, who hit a shot from just outside the penalty area, taking a slight deflection on its way.
A minute after McGaw's dismissal, Gavin Rothery put Leeds 2-0 up, but Stoke nearly hit back when Stephen Opoka's six-yard header, from Jimmy Phillips's right-wing cross, was tipped over the bar by Leeds keeper Knight.
Thompson capped his performance by curling home a trademark free-kick in the 35th minute before being withdrawn at half-time with Stoke trailing 3-0 and there was no respite for the visitors after the break as Leeds kept the pressure on and added a 50th-minute penalty from Tomi Ameobi.
With 12 minutes remaining, Howson got his second and Leeds's fifth with a firm shot following a right-wing cross to complete Stoke's misery.
The Whites: Knight, Hutton (Ovington 72), Fisher, Thompson (Hotchkiss 46), Wilkinson, Grace, Gardner, Howson, Ameobi (Elliott 76), Rothery, Rose.
Subs not used: Cartman, Vermooten
City: St Louis-Hamilton, Doyle, Watson, Keys (Brunt 70), Kangana (Williams 75) Robinson, Phillips, Grocott, Opoka (McCormack 83), Fordyce, McGaw. Subs not used: Kalipha, Ryan.